4 This chapter documents the statistical procedures that @pspp{} supports so
8 * DESCRIPTIVES:: Descriptive statistics.
9 * FREQUENCIES:: Frequency tables.
10 * EXAMINE:: Testing data for normality.
11 * CORRELATIONS:: Correlation tables.
12 * CROSSTABS:: Crosstabulation tables.
13 * FACTOR:: Factor analysis and Principal Components analysis
14 * MEANS:: Average values and other statistics.
15 * NPAR TESTS:: Nonparametric tests.
16 * T-TEST:: Test hypotheses about means.
17 * ONEWAY:: One way analysis of variance.
18 * QUICK CLUSTER:: K-Means clustering.
19 * RANK:: Compute rank scores.
20 * REGRESSION:: Linear regression.
21 * RELIABILITY:: Reliability analysis.
22 * ROC:: Receiver Operating Characteristic.
31 /VARIABLES=@var{var_list}
32 /MISSING=@{VARIABLE,LISTWISE@} @{INCLUDE,NOINCLUDE@}
33 /FORMAT=@{LABELS,NOLABELS@} @{NOINDEX,INDEX@} @{LINE,SERIAL@}
35 /STATISTICS=@{ALL,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,
36 SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,DEFAULT,
37 SESKEWNESS,SEKURTOSIS@}
38 /SORT=@{NONE,MEAN,SEMEAN,STDDEV,VARIANCE,KURTOSIS,SKEWNESS,
39 RANGE,MINIMUM,MAXIMUM,SUM,SESKEWNESS,SEKURTOSIS,NAME@}
43 The @cmd{DESCRIPTIVES} procedure reads the active dataset and outputs
45 statistics requested by the user. In addition, it can optionally
48 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
49 variables to be analyzed. Keyword @subcmd{VARIABLES} is optional.
51 All other subcommands are optional:
53 The @subcmd{MISSING} subcommand determines the handling of missing variables. If
54 @subcmd{INCLUDE} is set, then user-missing values are included in the
55 calculations. If @subcmd{NOINCLUDE} is set, which is the default, user-missing
56 values are excluded. If @subcmd{VARIABLE} is set, then missing values are
57 excluded on a variable by variable basis; if @subcmd{LISTWISE} is set, then
58 the entire case is excluded whenever any value in that case has a
59 system-missing or, if @subcmd{INCLUDE} is set, user-missing value.
61 The @subcmd{FORMAT} subcommand affects the output format. Currently the
62 @subcmd{LABELS/NOLABELS} and @subcmd{NOINDEX/INDEX} settings are not used.
63 When @subcmd{SERIAL} is
64 set, both valid and missing number of cases are listed in the output;
65 when @subcmd{NOSERIAL} is set, only valid cases are listed.
67 The @subcmd{SAVE} subcommand causes @cmd{DESCRIPTIVES} to calculate Z scores for all
68 the specified variables. The Z scores are saved to new variables.
69 Variable names are generated by trying first the original variable name
70 with Z prepended and truncated to a maximum of 8 characters, then the
71 names ZSC000 through ZSC999, STDZ00 through STDZ09, ZZZZ00 through
72 ZZZZ09, ZQZQ00 through ZQZQ09, in that sequence. In addition, Z score
73 variable names can be specified explicitly on @subcmd{VARIABLES} in the variable
74 list by enclosing them in parentheses after each variable.
76 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
80 All of the statistics below.
84 Standard error of the mean.
90 Kurtosis and standard error of the kurtosis.
92 Skewness and standard error of the skewness.
102 Mean, standard deviation of the mean, minimum, maximum.
104 Standard error of the kurtosis.
106 Standard error of the skewness.
109 The @subcmd{SORT} subcommand specifies how the statistics should be sorted. Most
110 of the possible values should be self-explanatory. @subcmd{NAME} causes the
111 statistics to be sorted by name. By default, the statistics are listed
112 in the order that they are specified on the @subcmd{VARIABLES} subcommand.
113 The @subcmd{A} and @subcmd{D} settings request an ascending or descending
114 sort order, respectively.
122 /VARIABLES=@var{var_list}
123 /FORMAT=@{TABLE,NOTABLE,LIMIT(@var{limit})@}
124 @{AVALUE,DVALUE,AFREQ,DFREQ@}
125 /MISSING=@{EXCLUDE,INCLUDE@}
126 /STATISTICS=@{DEFAULT,MEAN,SEMEAN,MEDIAN,MODE,STDDEV,VARIANCE,
127 KURTOSIS,SKEWNESS,RANGE,MINIMUM,MAXIMUM,SUM,
128 SESKEWNESS,SEKURTOSIS,ALL,NONE@}
130 /PERCENTILES=percent@dots{}
131 /HISTOGRAM=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
132 [@{FREQ[(@var{y_max})],PERCENT[(@var{y_max})]@}] [@{NONORMAL,NORMAL@}]
133 /PIECHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})]
134 [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}]
136 (These options are not currently implemented.)
142 The @cmd{FREQUENCIES} procedure outputs frequency tables for specified
144 @cmd{FREQUENCIES} can also calculate and display descriptive statistics
145 (including median and mode) and percentiles,
146 @cmd{FREQUENCIES} can also output
147 histograms and pie charts.
149 The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the
150 variables to be analyzed.
152 The @subcmd{FORMAT} subcommand controls the output format. It has several
157 @subcmd{TABLE}, the default, causes a frequency table to be output for every
158 variable specified. @subcmd{NOTABLE} prevents them from being output. @subcmd{LIMIT}
159 with a numeric argument causes them to be output except when there are
160 more than the specified number of values in the table.
163 Normally frequency tables are sorted in ascending order by value. This
164 is @subcmd{AVALUE}. @subcmd{DVALUE} tables are sorted in descending order by value.
165 @subcmd{AFREQ} and @subcmd{DFREQ} tables are sorted in ascending and descending order,
166 respectively, by frequency count.
169 The @subcmd{MISSING} subcommand controls the handling of user-missing values.
170 When @subcmd{EXCLUDE}, the default, is set, user-missing values are not included
171 in frequency tables or statistics. When @subcmd{INCLUDE} is set, user-missing
172 are included. System-missing values are never included in statistics,
173 but are listed in frequency tables.
175 The available @subcmd{STATISTICS} are the same as available
176 in @cmd{DESCRIPTIVES} (@pxref{DESCRIPTIVES}), with the addition
177 of @subcmd{MEDIAN}, the data's median
178 value, and MODE, the mode. (If there are multiple modes, the smallest
179 value is reported.) By default, the mean, standard deviation of the
180 mean, minimum, and maximum are reported for each variable.
183 @subcmd{PERCENTILES} causes the specified percentiles to be reported.
184 The percentiles should be presented at a list of numbers between 0
186 The @subcmd{NTILES} subcommand causes the percentiles to be reported at the
187 boundaries of the data set divided into the specified number of ranges.
188 For instance, @subcmd{/NTILES=4} would cause quartiles to be reported.
191 The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for
192 each specified numeric variable. The X axis by default ranges from
193 the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM}
194 and @subcmd{MAXIMUM} keywords can set an explicit range. Specify @subcmd{NORMAL} to
195 superimpose a normal curve on the histogram. Histograms are not
196 created for string variables.
199 The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each
200 slice represents one value, with the size of the slice proportional to
201 the value's frequency. By default, all non-missing values are given
202 slices. The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the
203 displayed slices to a given range of values. The @subcmd{MISSING} keyword adds
204 slices for missing values.
206 The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and @subcmd{PIECHART} are accepted
207 but not currently honoured.
213 @cindex Exploratory data analysis
214 @cindex Normality, testing for
218 VARIABLES= @var{var1} [@var{var2}] @dots{} [@var{varN}]
219 [BY @var{factor1} [BY @var{subfactor1}]
220 [ @var{factor2} [BY @var{subfactor2}]]
222 [ @var{factor3} [BY @var{subfactor3}]]
224 /STATISTICS=@{DESCRIPTIVES, EXTREME[(@var{n})], ALL, NONE@}
225 /PLOT=@{BOXPLOT, NPPLOT, HISTOGRAM, SPREADLEVEL[(@var{t})], ALL, NONE@}
227 /COMPARE=@{GROUPS,VARIABLES@}
228 /ID=@var{identity_variable}
230 /PERCENTILE=[@var{percentiles}]=@{HAVERAGE, WAVERAGE, ROUND, AEMPIRICAL, EMPIRICAL @}
231 /MISSING=@{LISTWISE, PAIRWISE@} [@{EXCLUDE, INCLUDE@}]
232 [@{NOREPORT,REPORT@}]
236 The @cmd{EXAMINE} command is used to perform exploratory data analysis.
237 In particular, it is useful for testing how closely a distribution follows a
238 normal distribution, and for finding outliers and extreme values.
240 The @subcmd{VARIABLES} subcommand is mandatory.
241 It specifies the dependent variables and optionally variables to use as
242 factors for the analysis.
243 Variables listed before the first @subcmd{BY} keyword (if any) are the
245 The dependent variables may optionally be followed by a list of
246 factors which tell @pspp{} how to break down the analysis for each
249 Following the dependent variables, factors may be specified.
250 The factors (if desired) should be preceeded by a single @subcmd{BY} keyword.
251 The format for each factor is
253 @var{factorvar} [BY @var{subfactorvar}].
255 Each unique combination of the values of @var{factorvar} and
256 @var{subfactorvar} divide the dataset into @dfn{cells}.
257 Statistics will be calculated for each cell
258 and for the entire dataset (unless @subcmd{NOTOTAL} is given).
260 The @subcmd{STATISTICS} subcommand specifies which statistics to show.
261 @subcmd{DESCRIPTIVES} will produce a table showing some parametric and
262 non-parametrics statistics.
263 @subcmd{EXTREME} produces a table showing the extremities of each cell.
264 A number in parentheses, @var{n} determines
265 how many upper and lower extremities to show.
266 The default number is 5.
268 The subcommands @subcmd{TOTAL} and @subcmd{NOTOTAL} are mutually exclusive.
269 If @subcmd{TOTAL} appears, then statistics will be produced for the entire dataset
270 as well as for each cell.
271 If @subcmd{NOTOTAL} appears, then statistics will be produced only for the cells
272 (unless no factor variables have been given).
273 These subcommands have no effect if there have been no factor variables
279 @cindex spreadlevel plot
280 The @subcmd{PLOT} subcommand specifies which plots are to be produced if any.
281 Available plots are @subcmd{HISTOGRAM}, @subcmd{NPPLOT}, @subcmd{BOXPLOT} and
282 @subcmd{SPREADLEVEL}.
283 The first three can be used to visualise how closely each cell conforms to a
284 normal distribution, whilst the spread vs.@: level plot can be useful to visualise
285 how the variance of differs between factors.
286 Boxplots will also show you the outliers and extreme values.
288 The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the
289 median. It takes an optional parameter @var{t}, which specifies how the data
290 should be transformed prior to plotting.
291 The given value @var{t} is a power to which the data is raised. For example, if
292 @var{t} is given as 2, then the data will be squared.
293 Zero, however is a special value. If @var{t} is 0 or
294 is omitted, then data will be transformed by taking its natural logarithm instead of
295 raising to the power of @var{t}.
297 The @subcmd{COMPARE} subcommand is only relevant if producing boxplots, and it is only
298 useful there is more than one dependent variable and at least one factor.
300 @subcmd{/COMPARE=GROUPS} is specified, then one plot per dependent variable is produced,
301 each of which contain boxplots for all the cells.
302 If @subcmd{/COMPARE=VARIABLES} is specified, then one plot per cell is produced,
303 each containing one boxplot per dependent variable.
304 If the @subcmd{/COMPARE} subcommand is omitted, then @pspp{} behaves as if
305 @subcmd{/COMPARE=GROUPS} were given.
307 The @subcmd{ID} subcommand is relevant only if @subcmd{/PLOT=BOXPLOT} or
308 @subcmd{/STATISTICS=EXTREME} has been given.
309 If given, it shoule provide the name of a variable which is to be used
310 to labels extreme values and outliers.
311 Numeric or string variables are permissible.
312 If the @subcmd{ID} subcommand is not given, then the casenumber will be used for
315 The @subcmd{CINTERVAL} subcommand specifies the confidence interval to use in
316 calculation of the descriptives command. The default is 95%.
319 The @subcmd{PERCENTILES} subcommand specifies which percentiles are to be calculated,
320 and which algorithm to use for calculating them. The default is to
321 calculate the 5, 10, 25, 50, 75, 90, 95 percentiles using the
322 @subcmd{HAVERAGE} algorithm.
324 The @subcmd{TOTAL} and @subcmd{NOTOTAL} subcommands are mutually exclusive. If @subcmd{NOTOTAL}
325 is given and factors have been specified in the @subcmd{VARIABLES} subcommand,
326 then then statistics for the unfactored dependent variables are
327 produced in addition to the factored variables. If there are no
328 factors specified then @subcmd{TOTAL} and @subcmd{NOTOTAL} have no effect.
331 The following example will generate descriptive statistics and histograms for
332 two variables @var{score1} and @var{score2}.
333 Two factors are given, @i{viz}: @var{gender} and @var{gender} BY @var{culture}.
334 Therefore, the descriptives and histograms will be generated for each
336 of @var{gender} @emph{and} for each distinct combination of the values
337 of @var{gender} and @var{race}.
338 Since the @subcmd{NOTOTAL} keyword is given, statistics and histograms for
339 @var{score1} and @var{score2} covering the whole dataset are not produced.
341 EXAMINE @var{score1} @var{score2} BY
343 @var{gender} BY @var{culture}
344 /STATISTICS = DESCRIPTIVES
349 Here is a second example showing how the @cmd{examine} command can be used to find extremities.
351 EXAMINE @var{height} @var{weight} BY
353 /STATISTICS = EXTREME (3)
358 In this example, we look at the height and weight of a sample of individuals and
359 how they differ between male and female.
360 A table showing the 3 largest and the 3 smallest values of @var{height} and
361 @var{weight} for each gender, and for the whole dataset will be shown.
362 Boxplots will also be produced.
363 Because @subcmd{/COMPARE = GROUPS} was given, boxplots for male and female will be
364 shown in the same graphic, allowing us to easily see the difference between
366 Since the variable @var{name} was specified on the @subcmd{ID} subcommand, this will be
367 used to label the extreme values.
370 If many dependent variables are specified, or if factor variables are
372 there are many distinct values, then @cmd{EXAMINE} will produce a very
373 large quantity of output.
376 @section CORRELATIONS
381 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
386 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
387 /VARIABLES = @var{var_list} [ WITH @var{var_list} ]
390 [ /PRINT=@{TWOTAIL, ONETAIL@} @{SIG, NOSIG@} ]
391 [ /STATISTICS=DESCRIPTIVES XPROD ALL]
392 [ /MISSING=@{PAIRWISE, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
396 The @cmd{CORRELATIONS} procedure produces tables of the Pearson correlation coefficient
397 for a set of variables. The significance of the coefficients are also given.
399 At least one @subcmd{VARIABLES} subcommand is required. If the @subcmd{WITH}
400 keyword is used, then a non-square correlation table will be produced.
401 The variables preceding @subcmd{WITH}, will be used as the rows of the table,
402 and the variables following will be the columns of the table.
403 If no @subcmd{WITH} subcommand is given, then a square, symmetrical table using all variables is produced.
406 The @cmd{MISSING} subcommand determines the handling of missing variables.
407 If @subcmd{INCLUDE} is set, then user-missing values are included in the
408 calculations, but system-missing values are not.
409 If @subcmd{EXCLUDE} is set, which is the default, user-missing
410 values are excluded as well as system-missing values.
413 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
414 whenever any variable specified in any @cmd{/VARIABLES} subcommand
415 contains a missing value.
416 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
417 values for the particular coefficient are missing.
418 The default is @subcmd{PAIRWISE}.
420 The @subcmd{PRINT} subcommand is used to control how the reported significance values are printed.
421 If the @subcmd{TWOTAIL} option is used, then a two-tailed test of significance is
422 printed. If the @subcmd{ONETAIL} option is given, then a one-tailed test is used.
423 The default is @subcmd{TWOTAIL}.
425 If the @subcmd{NOSIG} option is specified, then correlation coefficients with significance less than
426 0.05 are highlighted.
427 If @subcmd{SIG} is specified, then no highlighting is performed. This is the default.
430 The @subcmd{STATISTICS} subcommand requests additional statistics to be displayed. The keyword
431 @subcmd{DESCRIPTIVES} requests that the mean, number of non-missing cases, and the non-biased
432 estimator of the standard deviation are displayed.
433 These statistics will be displayed in a separated table, for all the variables listed
434 in any @subcmd{/VARIABLES} subcommand.
435 The @subcmd{XPROD} keyword requests cross-product deviations and covariance estimators to
436 be displayed for each pair of variables.
437 The keyword @subcmd{ALL} is the union of @subcmd{DESCRIPTIVES} and @subcmd{XPROD}.
445 /TABLES=@var{var_list} BY @var{var_list} [BY @var{var_list}]@dots{}
446 /MISSING=@{TABLE,INCLUDE,REPORT@}
447 /WRITE=@{NONE,CELLS,ALL@}
448 /FORMAT=@{TABLES,NOTABLES@}
453 /CELLS=@{COUNT,ROW,COLUMN,TOTAL,EXPECTED,RESIDUAL,SRESIDUAL,
454 ASRESIDUAL,ALL,NONE@}
455 /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D,
456 KAPPA,ETA,CORR,ALL,NONE@}
459 /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{}
462 The @cmd{CROSSTABS} procedure displays crosstabulation
463 tables requested by the user. It can calculate several statistics for
464 each cell in the crosstabulation tables. In addition, a number of
465 statistics can be calculated for each table itself.
467 The @subcmd{TABLES} subcommand is used to specify the tables to be reported. Any
468 number of dimensions is permitted, and any number of variables per
469 dimension is allowed. The @subcmd{TABLES} subcommand may be repeated as many
470 times as needed. This is the only required subcommand in @dfn{general
473 Occasionally, one may want to invoke a special mode called @dfn{integer
474 mode}. Normally, in general mode, @pspp{} automatically determines
475 what values occur in the data. In integer mode, the user specifies the
476 range of values that the data assumes. To invoke this mode, specify the
477 @subcmd{VARIABLES} subcommand, giving a range of data values in parentheses for
478 each variable to be used on the @subcmd{TABLES} subcommand. Data values inside
479 the range are truncated to the nearest integer, then assigned to that
480 value. If values occur outside this range, they are discarded. When it
481 is present, the @subcmd{VARIABLES} subcommand must precede the @subcmd{TABLES}
484 In general mode, numeric and string variables may be specified on
485 TABLES. In integer mode, only numeric variables are allowed.
487 The @subcmd{MISSING} subcommand determines the handling of user-missing values.
488 When set to @subcmd{TABLE}, the default, missing values are dropped on a table by
489 table basis. When set to @subcmd{INCLUDE}, user-missing values are included in
490 tables and statistics. When set to @subcmd{REPORT}, which is allowed only in
491 integer mode, user-missing values are included in tables but marked with
492 an @samp{M} (for ``missing'') and excluded from statistical
495 Currently the @subcmd{WRITE} subcommand is ignored.
497 The @subcmd{FORMAT} subcommand controls the characteristics of the
498 crosstabulation tables to be displayed. It has a number of possible
503 @subcmd{TABLES}, the default, causes crosstabulation tables to be output.
504 @subcmd{NOTABLES} suppresses them.
507 @subcmd{PIVOT}, the default, causes each @subcmd{TABLES} subcommand to be displayed in a
508 pivot table format. @subcmd{NOPIVOT} causes the old-style crosstabulation format
512 @subcmd{AVALUE}, the default, causes values to be sorted in ascending order.
513 @subcmd{DVALUE} asserts a descending sort order.
516 @subcmd{INDEX} and @subcmd{NOINDEX} are currently ignored.
519 @subcmd{BOX} and @subcmd{NOBOX} is currently ignored.
522 The @subcmd{CELLS} subcommand controls the contents of each cell in the displayed
523 crosstabulation table. The possible settings are:
539 Standardized residual.
541 Adjusted standardized residual.
545 Suppress cells entirely.
548 @samp{/CELLS} without any settings specified requests @subcmd{COUNT}, @subcmd{ROW},
549 @subcmd{COLUMN}, and @subcmd{TOTAL}.
550 If @subcmd{CELLS} is not specified at all then only @subcmd{COUNT}
553 The @subcmd{STATISTICS} subcommand selects statistics for computation:
560 Pearson chi-square, likelihood ratio, Fisher's exact test, continuity
561 correction, linear-by-linear association.
565 Contingency coefficient.
569 Uncertainty coefficient.
585 Spearman correlation, Pearson's r.
592 Selected statistics are only calculated when appropriate for the
593 statistic. Certain statistics require tables of a particular size, and
594 some statistics are calculated only in integer mode.
596 @samp{/STATISTICS} without any settings selects CHISQ. If the
597 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
599 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
604 Pearson's R (but not Spearman) is off a little.
606 T values for Spearman's R and Pearson's R are wrong.
608 Significance of symmetric and directional measures is not calculated.
610 Asymmetric ASEs and T values for lambda are wrong.
612 ASE of Goodman and Kruskal's tau is not calculated.
614 ASE of symmetric somers' d is wrong.
616 Approximate T of uncertainty coefficient is wrong.
619 Fixes for any of these deficiencies would be welcomed.
625 @cindex factor analysis
626 @cindex principal components analysis
627 @cindex principal axis factoring
628 @cindex data reduction
631 FACTOR VARIABLES=@var{var_list}
633 [ /METHOD = @{CORRELATION, COVARIANCE@} ]
635 [ /EXTRACTION=@{PC, PAF@}]
637 [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, NOROTATE@}]
639 [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [SIG] [ALL] [DEFAULT] ]
643 [ /FORMAT=[SORT] [BLANK(@var{n})] [DEFAULT] ]
645 [ /CRITERIA=[FACTORS(@var{n})] [MINEIGEN(@var{l})] [ITERATE(@var{m})] [ECONVERGE (@var{delta})] [DEFAULT] ]
647 [ /MISSING=[@{LISTWISE, PAIRWISE@}] [@{INCLUDE, EXCLUDE@}] ]
650 The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find
651 common factors in the data or for data reduction purposes.
653 The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis.
655 The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data.
656 If @subcmd{PC} is specified, then Principal Components Analysis is used.
657 If @subcmd{PAF} is specified, then Principal Axis Factoring is
658 used. By default Principal Components Analysis will be used.
660 The @subcmd{/ROTATION} subcommand is used to specify the method by which the extracted solution will be rotated.
661 Three methods are available: @subcmd{VARIMAX} (which is the default), @subcmd{EQUAMAX}, and @subcmd{QUARTIMAX}.
662 If don't want any rotation to be performed, the word @subcmd{NOROTATE} will prevent the command from performing any
663 rotation on the data. Oblique rotations are not supported.
665 The @subcmd{/METHOD} subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is
666 to be analysed. By default, the correlation matrix is analysed.
668 The @subcmd{/PRINT} subcommand may be used to select which features of the analysis are reported:
672 A table of mean values, standard deviations and total weights are printed.
674 Initial communalities and eigenvalues are printed.
676 Extracted communalities and eigenvalues are printed.
678 Rotated communalities and eigenvalues are printed.
680 The correlation matrix is printed.
682 The covariance matrix is printed.
684 The determinant of the correlation or covariance matrix is printed.
686 The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
688 The significance of the elements of correlation matrix is printed.
690 All of the above are printed.
692 Identical to @subcmd{INITIAL} and @subcmd{EXTRACTION}.
695 If @subcmd{/PLOT=EIGEN} is given, then a ``Scree'' plot of the eigenvalues will be printed. This can be useful for visualizing
696 which factors (components) should be retained.
698 The @subcmd{/FORMAT} subcommand determined how data are to be displayed in loading matrices. If @subcmd{SORT} is specified, then the variables
699 are sorted in descending order of significance. If @subcmd{BLANK(@var{n})} is specified, then coefficients whose absolute value is less
700 than @var{n} will not be printed. If the keyword @subcmd{DEFAULT} is given, or if no @subcmd{/FORMAT} subcommand is given, then no sorting is
701 performed, and all coefficients will be printed.
703 The @subcmd{/CRITERIA} subcommand is used to specify how the number of extracted factors (components) are chosen.
704 If @subcmd{FACTORS(@var{n})} is
705 specified, where @var{n} is an integer, then @var{n} factors will be extracted. Otherwise, the @subcmd{MINEIGEN} setting will
706 be used. @subcmd{MINEIGEN(@var{l})} requests that all factors whose eigenvalues are greater than or equal to @var{l} are extracted.
707 The default value of @var{l} is 1. The @subcmd{ECONVERGE} and @subcmd{ITERATE} settings have effect only when iterative algorithms for factor
708 extraction (such as Principal Axis Factoring) are used. @subcmd{ECONVERGE(@var{delta})} specifies that
709 iteration should cease when
710 the maximum absolute value of the communality estimate between one iteration and the previous is less than @var{delta}. The
711 default value of @var{delta} is 0.001.
712 The @subcmd{ITERATE(@var{m})} setting sets the maximum number of iterations to @var{m}. The default value of @var{m} is 25.
714 The @cmd{MISSING} subcommand determines the handling of missing variables.
715 If @subcmd{INCLUDE} is set, then user-missing values are included in the
716 calculations, but system-missing values are not.
717 If @subcmd{EXCLUDE} is set, which is the default, user-missing
718 values are excluded as well as system-missing values.
720 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
721 whenever any variable specified in the @cmd{VARIABLES} subcommand
722 contains a missing value.
723 If @subcmd{PAIRWISE} is set, then a case is considered missing only if either of the
724 values for the particular coefficient are missing.
725 The default is @subcmd{LISTWISE}.
736 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]]
738 [ /@{@var{var_list}@}
739 [ BY @{@var{var_list}@} [BY @{@var{var_list}@} [BY @{@var{var_list}@} @dots{} ]]] ]
741 [/CELLS = [MEAN] [COUNT] [STDDEV] [SEMEAN] [SUM] [MIN] [MAX] [RANGE]
742 [VARIANCE] [KURT] [SEKURT]
743 [SKEW] [SESKEW] [FIRST] [LAST]
744 [HARMONIC] [GEOMETRIC]
749 [/MISSING = [TABLE] [INCLUDE] [DEPENDENT]]
752 You can use the @cmd{MEANS} command to calculate the arithmetic mean and similar
753 statistics, either for the dataset as a whole or for categories of data.
755 The simplest form of the command is
759 @noindent which calculates the mean, count and standard deviation for @var{v}.
760 If you specify a grouping variable, for example
762 MEANS @var{v} BY @var{g}.
764 @noindent then the means, counts and standard deviations for @var{v} after having
765 been grouped by @var{g} will be calculated.
766 Instead of the mean, count and standard deviation, you could specify the statistics
767 in which you are interested:
769 MEANS @var{x} @var{y} BY @var{g}
770 /CELLS = HARMONIC SUM MIN.
772 This example calculates the harmonic mean, the sum and the minimum values of @var{x} and @var{y}
775 The @subcmd{CELLS} subcommand specifies which statistics to calculate. The available statistics
779 @cindex arithmetic mean
782 The count of the values.
783 @item @subcmd{STDDEV}
784 The standard deviation.
785 @item @subcmd{SEMEAN}
786 The standard error of the mean.
788 The sum of the values.
794 The difference between the maximum and minimum values.
795 @item @subcmd{VARIANCE}
798 The first value in the category.
800 The last value in the category.
803 @item @subcmd{SESKEW}
804 The standard error of the skewness.
807 @item @subcmd{SEKURT}
808 The standard error of the kurtosis.
809 @item @subcmd{HARMONIC}
810 @cindex harmonic mean
812 @item @subcmd{GEOMETRIC}
813 @cindex geometric mean
817 In addition, three special keywords are recognized:
819 @item @subcmd{DEFAULT}
820 This is the same as @subcmd{MEAN} @subcmd{COUNT} @subcmd{STDDEV}.
822 All of the above statistics will be calculated.
824 No statistics will be calculated (only a summary will be shown).
828 More than one @dfn{table} can be specified in a single command.
829 Each table is separated by a @samp{/}. For
833 @var{c} @var{d} @var{e} BY @var{x}
834 /@var{a} @var{b} BY @var{x} @var{y}
835 /@var{f} BY @var{y} BY @var{z}.
837 has three tables (the @samp{TABLE =} is optional).
838 The first table has three dependent variables @var{c}, @var{d} and @var{e}
839 and a single categorical variable @var{x}.
840 The second table has two dependent variables @var{a} and @var{b},
841 and two categorical variables @var{x} and @var{y}.
842 The third table has a single dependent variables @var{f}
843 and a categorical variable formed by the combination of @var{y} and @var{z}.
846 By default values are omitted from the analysis only if missing values
847 (either system missing or user missing)
848 for any of the variables directly involved in their calculation are
850 This behaviour can be modified with the @subcmd{/MISSING} subcommand.
851 Three options are possible: @subcmd{TABLE}, @subcmd{INCLUDE} and @subcmd{DEPENDENT}.
853 @subcmd{/MISSING = TABLE} causes cases to be dropped if any variable is missing
854 in the table specification currently being processed, regardless of
855 whether it is needed to calculate the statistic.
857 @subcmd{/MISSING = INCLUDE} says that user missing values, either in the dependent
858 variables or in the categorical variables should be taken at their face
859 value, and not excluded.
861 @subcmd{/MISSING = DEPENDENT} says that user missing values, in the dependent
862 variables should be taken at their face value, however cases which
863 have user missing values for the categorical variables should be omitted
864 from the calculation.
870 @cindex nonparametric tests
875 nonparametric test subcommands
880 [ /STATISTICS=@{DESCRIPTIVES@} ]
882 [ /MISSING=@{ANALYSIS, LISTWISE@} @{INCLUDE, EXCLUDE@} ]
884 [ /METHOD=EXACT [ TIMER [(@var{n})] ] ]
887 @cmd{NPAR TESTS} performs nonparametric tests.
888 Non parametric tests make very few assumptions about the distribution of the
890 One or more tests may be specified by using the corresponding subcommand.
891 If the @subcmd{/STATISTICS} subcommand is also specified, then summary statistics are
892 produces for each variable that is the subject of any test.
894 Certain tests may take a long time to execute, if an exact figure is required.
895 Therefore, by default asymptotic approximations are used unless the
896 subcommand @subcmd{/METHOD=EXACT} is specified.
897 Exact tests give more accurate results, but may take an unacceptably long
898 time to perform. If the @subcmd{TIMER} keyword is used, it sets a maximum time,
899 after which the test will be abandoned, and a warning message printed.
900 The time, in minutes, should be specified in parentheses after the @subcmd{TIMER} keyword.
901 If the @subcmd{TIMER} keyword is given without this figure, then a default value of 5 minutes
906 * BINOMIAL:: Binomial Test
907 * CHISQUARE:: Chisquare Test
908 * COCHRAN:: Cochran Q Test
909 * FRIEDMAN:: Friedman Test
910 * KENDALL:: Kendall's W Test
911 * KOLMOGOROV-SMIRNOV:: Kolmogorov Smirnov Test
912 * KRUSKAL-WALLIS:: Kruskal-Wallis Test
913 * MANN-WHITNEY:: Mann Whitney U Test
914 * MCNEMAR:: McNemar Test
915 * MEDIAN:: Median Test
917 * SIGN:: The Sign Test
918 * WILCOXON:: Wilcoxon Signed Ranks Test
923 @subsection Binomial test
925 @cindex binomial test
928 [ /BINOMIAL[(@var{p})]=@var{var_list}[(@var{value1}[, @var{value2})] ] ]
931 The @subcmd{/BINOMIAL} subcommand compares the observed distribution of a dichotomous
932 variable with that of a binomial distribution.
933 The variable @var{p} specifies the test proportion of the binomial
935 The default value of 0.5 is assumed if @var{p} is omitted.
937 If a single value appears after the variable list, then that value is
938 used as the threshold to partition the observed values. Values less
939 than or equal to the threshold value form the first category. Values
940 greater than the threshold form the second category.
942 If two values appear after the variable list, then they will be used
943 as the values which a variable must take to be in the respective
945 Cases for which a variable takes a value equal to neither of the specified
946 values, take no part in the test for that variable.
948 If no values appear, then the variable must assume dichotomous
950 If more than two distinct, non-missing values for a variable
951 under test are encountered then an error occurs.
953 If the test proportion is equal to 0.5, then a two tailed test is
954 reported. For any other test proportion, a one tailed test is
956 For one tailed tests, if the test proportion is less than
957 or equal to the observed proportion, then the significance of
958 observing the observed proportion or more is reported.
959 If the test proportion is more than the observed proportion, then the
960 significance of observing the observed proportion or less is reported.
961 That is to say, the test is always performed in the observed
964 @pspp{} uses a very precise approximation to the gamma function to
965 compute the binomial significance. Thus, exact results are reported
966 even for very large sample sizes.
971 @subsection Chisquare Test
973 @cindex chisquare test
977 [ /CHISQUARE=@var{var_list}[(@var{lo},@var{hi})] [/EXPECTED=@{EQUAL|@var{f1}, @var{f2} @dots{} @var{fn}@}] ]
981 The @subcmd{/CHISQUARE} subcommand produces a chi-square statistic for the differences
982 between the expected and observed frequencies of the categories of a variable.
983 Optionally, a range of values may appear after the variable list.
984 If a range is given, then non integer values are truncated, and values
985 outside the specified range are excluded from the analysis.
987 The @subcmd{/EXPECTED} subcommand specifies the expected values of each
989 There must be exactly one non-zero expected value, for each observed
990 category, or the @subcmd{EQUAL} keywork must be specified.
991 You may use the notation @subcmd{@var{n}*@var{f}} to specify @var{n}
992 consecutive expected categories all taking a frequency of @var{f}.
993 The frequencies given are proportions, not absolute frequencies. The
994 sum of the frequencies need not be 1.
995 If no @subcmd{/EXPECTED} subcommand is given, then then equal frequencies
1000 @subsection Cochran Q Test
1002 @cindex Cochran Q test
1003 @cindex Q, Cochran Q
1006 [ /COCHRAN = @var{var_list} ]
1009 The Cochran Q test is used to test for differences between three or more groups.
1010 The data for @var{var_list} in all cases must assume exactly two distinct values (other than missing values).
1012 The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution.
1015 @subsection Friedman Test
1017 @cindex Friedman test
1020 [ /FRIEDMAN = @var{var_list} ]
1023 The Friedman test is used to test for differences between repeated measures when
1024 there is no indication that the distributions are normally distributed.
1026 A list of variables which contain the measured data must be given. The procedure
1027 prints the sum of ranks for each variable, the test statistic and its significance.
1030 @subsection Kendall's W Test
1032 @cindex Kendall's W test
1033 @cindex coefficient of concordance
1036 [ /KENDALL = @var{var_list} ]
1039 The Kendall test investigates whether an arbitrary number of related samples come from the
1041 It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed.
1042 It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of
1043 unity indicates complete agreement.
1046 @node KOLMOGOROV-SMIRNOV
1047 @subsection Kolmogorov-Smirnov Test
1048 @vindex KOLMOGOROV-SMIRNOV
1050 @cindex Kolmogorov-Smirnov test
1053 [ /KOLMOGOROV-SMIRNOV (@{NORMAL [@var{mu}, @var{sigma}], UNIFORM [@var{min}, @var{max}], POISSON [@var{lambda}], EXPONENTIAL [@var{scale}] @}) = @var{var_list} ]
1056 The one sample Kolmogorov-Smirnov subcommand is used to test whether or not a dataset is
1057 drawn from a particular distribution. Four distributions are supported, @i{viz:}
1058 Normal, Uniform, Poisson and Exponential.
1060 Ideally you should provide the parameters of the distribution against which you wish to test
1061 the data. For example, with the normal distribution the mean (@var{mu})and standard deviation (@var{sigma})
1062 should be given; with the uniform distribution, the minimum (@var{min})and maximum (@var{max}) value should
1064 However, if the parameters are omitted they will be imputed from the data. Imputing the
1065 parameters reduces the power of the test so should be avoided if possible.
1067 In the following example, two variables @var{score} and @var{age} are tested to see if
1068 they follow a normal distribution with a mean of 3.5 and a standard deviation of 2.0.
1071 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score} @var{age}.
1073 If the variables need to be tested against different distributions, then a separate
1074 subcommand must be used. For example the following syntax tests @var{score} against
1075 a normal distribution with mean of 3.5 and standard deviation of 2.0 whilst @var{age}
1076 is tested against a normal distribution of mean 40 and standard deviation 1.5.
1079 /KOLMOGOROV-SMIRNOV (normal 3.5 2.0) = @var{score}
1080 /KOLMOGOROV-SMIRNOV (normal 40 1.5) = @var{age}.
1083 The abbreviated subcommand @subcmd{K-S} may be used in place of @subcmd{KOLMOGOROV-SMIRNOV}.
1085 @node KRUSKAL-WALLIS
1086 @subsection Kruskal-Wallis Test
1087 @vindex KRUSKAL-WALLIS
1089 @cindex Kruskal-Wallis test
1092 [ /KRUSKAL-WALLIS = @var{var_list} BY var (@var{lower}, @var{upper}) ]
1095 The Kruskal-Wallis test is used to compare data from an
1096 arbitrary number of populations. It does not assume normality.
1097 The data to be compared are specified by @var{var_list}.
1098 The categorical variable determining the groups to which the
1099 data belongs is given by @var{var}. The limits @var{lower} and
1100 @var{upper} specify the valid range of @var{var}. Any cases for
1101 which @var{var} falls outside [@var{lower}, @var{upper}] will be
1104 The mean rank of each group as well as the chi-squared value and significance
1105 of the test will be printed.
1106 The abbreviated subcommand @subcmd{K-W} may be used in place of @subcmd{KRUSKAL-WALLIS}.
1110 @subsection Mann-Whitney U Test
1111 @vindex MANN-WHITNEY
1113 @cindex Mann-Whitney U test
1114 @cindex U, Mann-Whitney U
1117 [ /MANN-WHITNEY = @var{var_list} BY var (@var{group1}, @var{group2}) ]
1120 The Mann-Whitney subcommand is used to test whether two groups of data come from different populations.
1121 The variables to be tested should be specified in @var{var_list} and the grouping variable, that determines to which group the test variables belong, in @var{var}.
1122 @var{Var} may be either a string or an alpha variable.
1123 @var{Group1} and @var{group2} specify the
1124 two values of @var{var} which determine the groups of the test data.
1125 Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored.
1127 The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed.
1128 The abbreviated subcommand @subcmd{M-W} may be used in place of @subcmd{MANN-WHITNEY}.
1131 @subsection McNemar Test
1133 @cindex McNemar test
1136 [ /MCNEMAR @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1139 Use McNemar's test to analyse the significance of the difference between
1140 pairs of correlated proportions.
1142 If the @code{WITH} keyword is omitted, then tests for all
1143 combinations of the listed variables are performed.
1144 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1145 is also given, then the number of variables preceding @code{WITH}
1146 must be the same as the number following it.
1147 In this case, tests for each respective pair of variables are
1149 If the @code{WITH} keyword is given, but the
1150 @code{(PAIRED)} keyword is omitted, then tests for each combination
1151 of variable preceding @code{WITH} against variable following
1152 @code{WITH} are performed.
1154 The data in each variable must be dichotomous. If there are more
1155 than two distinct variables an error will occur and the test will
1159 @subsection Median Test
1164 [ /MEDIAN [(@var{value})] = @var{var_list} BY @var{variable} (@var{value1}, @var{value2}) ]
1167 The median test is used to test whether independent samples come from
1168 populations with a common median.
1169 The median of the populations against which the samples are to be tested
1170 may be given in parentheses immediately after the
1171 @subcmd{/MEDIAN} subcommand. If it is not given, the median will be imputed from the
1172 union of all the samples.
1174 The variables of the samples to be tested should immediately follow the @samp{=} sign. The
1175 keyword @code{BY} must come next, and then the grouping variable. Two values
1176 in parentheses should follow. If the first value is greater than the second,
1177 then a 2 sample test is performed using these two values to determine the groups.
1178 If however, the first variable is less than the second, then a @i{k} sample test is
1179 conducted and the group values used are all values encountered which lie in the
1180 range [@var{value1},@var{value2}].
1184 @subsection Runs Test
1189 [ /RUNS (@{MEAN, MEDIAN, MODE, @var{value}@}) = @var{var_list} ]
1192 The @subcmd{/RUNS} subcommand tests whether a data sequence is randomly ordered.
1194 It works by examining the number of times a variable's value crosses a given threshold.
1195 The desired threshold must be specified within parentheses.
1196 It may either be specified as a number or as one of @subcmd{MEAN}, @subcmd{MEDIAN} or @subcmd{MODE}.
1197 Following the threshold specification comes the list of variables whose values are to be
1200 The subcommand shows the number of runs, the asymptotic significance based on the
1204 @subsection Sign Test
1209 [ /SIGN @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1212 The @subcmd{/SIGN} subcommand tests for differences between medians of the
1214 The test does not make any assumptions about the
1215 distribution of the data.
1217 If the @code{WITH} keyword is omitted, then tests for all
1218 combinations of the listed variables are performed.
1219 If the @code{WITH} keyword is given, and the @code{(PAIRED)} keyword
1220 is also given, then the number of variables preceding @code{WITH}
1221 must be the same as the number following it.
1222 In this case, tests for each respective pair of variables are
1224 If the @code{WITH} keyword is given, but the
1225 @code{(PAIRED)} keyword is omitted, then tests for each combination
1226 of variable preceding @code{WITH} against variable following
1227 @code{WITH} are performed.
1230 @subsection Wilcoxon Matched Pairs Signed Ranks Test
1232 @cindex wilcoxon matched pairs signed ranks test
1235 [ /WILCOXON @var{var_list} [ WITH @var{var_list} [ (PAIRED) ]]]
1238 The @subcmd{/WILCOXON} subcommand tests for differences between medians of the
1240 The test does not make any assumptions about the variances of the samples.
1241 It does however assume that the distribution is symetrical.
1243 If the @subcmd{WITH} keyword is omitted, then tests for all
1244 combinations of the listed variables are performed.
1245 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1246 is also given, then the number of variables preceding @subcmd{WITH}
1247 must be the same as the number following it.
1248 In this case, tests for each respective pair of variables are
1250 If the @subcmd{WITH} keyword is given, but the
1251 @subcmd{(PAIRED)} keyword is omitted, then tests for each combination
1252 of variable preceding @subcmd{WITH} against variable following
1253 @subcmd{WITH} are performed.
1262 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1263 /CRITERIA=CIN(@var{confidence})
1267 TESTVAL=@var{test_value}
1268 /VARIABLES=@var{var_list}
1271 (Independent Samples mode.)
1272 GROUPS=var(@var{value1} [, @var{value2}])
1273 /VARIABLES=@var{var_list}
1276 (Paired Samples mode.)
1277 PAIRS=@var{var_list} [WITH @var{var_list} [(PAIRED)] ]
1282 The @cmd{T-TEST} procedure outputs tables used in testing hypotheses about
1284 It operates in one of three modes:
1286 @item One Sample mode.
1287 @item Independent Groups mode.
1292 Each of these modes are described in more detail below.
1293 There are two optional subcommands which are common to all modes.
1295 The @cmd{/CRITERIA} subcommand tells @pspp{} the confidence interval used
1296 in the tests. The default value is 0.95.
1299 The @cmd{MISSING} subcommand determines the handling of missing
1301 If @subcmd{INCLUDE} is set, then user-missing values are included in the
1302 calculations, but system-missing values are not.
1303 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1304 values are excluded as well as system-missing values.
1305 This is the default.
1307 If @subcmd{LISTWISE} is set, then the entire case is excluded from analysis
1308 whenever any variable specified in the @subcmd{/VARIABLES}, @subcmd{/PAIRS} or
1309 @subcmd{/GROUPS} subcommands contains a missing value.
1310 If @subcmd{ANALYSIS} is set, then missing values are excluded only in the analysis for
1311 which they would be needed. This is the default.
1315 * One Sample Mode:: Testing against a hypothesized mean
1316 * Independent Samples Mode:: Testing two independent groups for equal mean
1317 * Paired Samples Mode:: Testing two interdependent groups for equal mean
1320 @node One Sample Mode
1321 @subsection One Sample Mode
1323 The @subcmd{TESTVAL} subcommand invokes the One Sample mode.
1324 This mode is used to test a population mean against a hypothesized
1326 The value given to the @subcmd{TESTVAL} subcommand is the value against
1327 which you wish to test.
1328 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1329 tell @pspp{} which variables you wish to test.
1331 @node Independent Samples Mode
1332 @subsection Independent Samples Mode
1334 The @subcmd{GROUPS} subcommand invokes Independent Samples mode or
1336 This mode is used to test whether two groups of values have the
1337 same population mean.
1338 In this mode, you must also use the @subcmd{/VARIABLES} subcommand to
1339 tell @pspp{} the dependent variables you wish to test.
1341 The variable given in the @subcmd{GROUPS} subcommand is the independent
1342 variable which determines to which group the samples belong.
1343 The values in parentheses are the specific values of the independent
1344 variable for each group.
1345 If the parentheses are omitted and no values are given, the default values
1346 of 1.0 and 2.0 are assumed.
1348 If the independent variable is numeric,
1349 it is acceptable to specify only one value inside the parentheses.
1350 If you do this, cases where the independent variable is
1351 greater than or equal to this value belong to the first group, and cases
1352 less than this value belong to the second group.
1353 When using this form of the @subcmd{GROUPS} subcommand, missing values in
1354 the independent variable are excluded on a listwise basis, regardless
1355 of whether @subcmd{/MISSING=LISTWISE} was specified.
1358 @node Paired Samples Mode
1359 @subsection Paired Samples Mode
1361 The @cmd{PAIRS} subcommand introduces Paired Samples mode.
1362 Use this mode when repeated measures have been taken from the same
1364 If the @subcmd{WITH} keyword is omitted, then tables for all
1365 combinations of variables given in the @cmd{PAIRS} subcommand are
1367 If the @subcmd{WITH} keyword is given, and the @subcmd{(PAIRED)} keyword
1368 is also given, then the number of variables preceding @subcmd{WITH}
1369 must be the same as the number following it.
1370 In this case, tables for each respective pair of variables are
1372 In the event that the @subcmd{WITH} keyword is given, but the
1373 @subcmd{(PAIRED)} keyword is omitted, then tables for each combination
1374 of variable preceding @subcmd{WITH} against variable following
1375 @subcmd{WITH} are generated.
1382 @cindex analysis of variance
1387 [/VARIABLES = ] @var{var_list} BY @var{var}
1388 /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@}
1389 /CONTRAST= @var{value1} [, @var{value2}] ... [,@var{valueN}]
1390 /STATISTICS=@{DESCRIPTIVES,HOMOGENEITY@}
1391 /POSTHOC=@{BONFERRONI, GH, LSD, SCHEFFE, SIDAK, TUKEY, ALPHA ([@var{value}])@}
1394 The @cmd{ONEWAY} procedure performs a one-way analysis of variance of
1395 variables factored by a single independent variable.
1396 It is used to compare the means of a population
1397 divided into more than two groups.
1399 The dependent variables to be analysed should be given in the @subcmd{VARIABLES}
1401 The list of variables must be followed by the @subcmd{BY} keyword and
1402 the name of the independent (or factor) variable.
1404 You can use the @subcmd{STATISTICS} subcommand to tell @pspp{} to display
1405 ancilliary information. The options accepted are:
1408 Displays descriptive statistics about the groups factored by the independent
1411 Displays the Levene test of Homogeneity of Variance for the
1412 variables and their groups.
1415 The @subcmd{CONTRAST} subcommand is used when you anticipate certain
1416 differences between the groups.
1417 The subcommand must be followed by a list of numerals which are the
1418 coefficients of the groups to be tested.
1419 The number of coefficients must correspond to the number of distinct
1420 groups (or values of the independent variable).
1421 If the total sum of the coefficients are not zero, then @pspp{} will
1422 display a warning, but will proceed with the analysis.
1423 The @subcmd{CONTRAST} subcommand may be given up to 10 times in order
1424 to specify different contrast tests.
1425 The @subcmd{MISSING} subcommand defines how missing values are handled.
1426 If @subcmd{LISTWISE} is specified then cases which have missing values for
1427 the independent variable or any dependent variable will be ignored.
1428 If @subcmd{ANALYSIS} is specified, then cases will be ignored if the independent
1429 variable is missing or if the dependent variable currently being
1430 analysed is missing. The default is @subcmd{ANALYSIS}.
1431 A setting of @subcmd{EXCLUDE} means that variables whose values are
1432 user-missing are to be excluded from the analysis. A setting of
1433 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1435 Using the @code{POSTHOC} subcommand you can perform multiple
1436 pairwise comparisons on the data. The following comparison methods
1440 Least Significant Difference.
1441 @item @subcmd{TUKEY}
1442 Tukey Honestly Significant Difference.
1443 @item @subcmd{BONFERRONI}
1445 @item @subcmd{SCHEFFE}
1447 @item @subcmd{SIDAK}
1450 The Games-Howell test.
1454 The optional syntax @code{ALPHA(@var{value})} is used to indicate
1455 that @var{value} should be used as the
1456 confidence level for which the posthoc tests will be performed.
1457 The default is 0.05.
1460 @section QUICK CLUSTER
1461 @vindex QUICK CLUSTER
1463 @cindex K-means clustering
1467 QUICK CLUSTER @var{var_list}
1468 [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]]
1469 [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}]
1472 The @cmd{QUICK CLUSTER} command performs k-means clustering on the
1473 dataset. This is useful when you wish to allocate cases into clusters
1474 of similar values and you already know the number of clusters.
1476 The minimum specification is @samp{QUICK CLUSTER} followed by the names
1477 of the variables which contain the cluster data. Normally you will also
1478 want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the
1479 number of clusters. If this is not given, then @var{k} defaults to 2.
1481 The command uses an iterative algorithm to determine the clusters for
1482 each case. It will continue iterating until convergence, or until @var{max_iter}
1483 iterations have been done. The default value of @var{max_iter} is 2.
1485 The @subcmd{MISSING} subcommand determines the handling of missing variables.
1486 If @subcmd{INCLUDE} is set, then user-missing values are considered at their face
1487 value and not as missing values.
1488 If @subcmd{EXCLUDE} is set, which is the default, user-missing
1489 values are excluded as well as system-missing values.
1491 If @subcmd{LISTWISE} is set, then the entire case is excluded from the analysis
1492 whenever any of the clustering variables contains a missing value.
1493 If @subcmd{PAIRWISE} is set, then a case is considered missing only if all the
1494 clustering variables contain missing values. Otherwise it is clustered
1495 on the basis of the non-missing values.
1496 The default is @subcmd{LISTWISE}.
1505 [VARIABLES=] @var{var_list} [@{A,D@}] [BY @var{var_list}]
1506 /TIES=@{MEAN,LOW,HIGH,CONDENSE@}
1507 /FRACTION=@{BLOM,TUKEY,VW,RANKIT@}
1509 /MISSING=@{EXCLUDE,INCLUDE@}
1511 /RANK [INTO @var{var_list}]
1512 /NTILES(k) [INTO @var{var_list}]
1513 /NORMAL [INTO @var{var_list}]
1514 /PERCENT [INTO @var{var_list}]
1515 /RFRACTION [INTO @var{var_list}]
1516 /PROPORTION [INTO @var{var_list}]
1517 /N [INTO @var{var_list}]
1518 /SAVAGE [INTO @var{var_list}]
1521 The @cmd{RANK} command ranks variables and stores the results into new
1524 The @subcmd{VARIABLES} subcommand, which is mandatory, specifies one or
1525 more variables whose values are to be ranked.
1526 After each variable, @samp{A} or @samp{D} may appear, indicating that
1527 the variable is to be ranked in ascending or descending order.
1528 Ascending is the default.
1529 If a @subcmd{BY} keyword appears, it should be followed by a list of variables
1530 which are to serve as group variables.
1531 In this case, the cases are gathered into groups, and ranks calculated
1534 The @subcmd{TIES} subcommand specifies how tied values are to be treated. The
1535 default is to take the mean value of all the tied cases.
1537 The @subcmd{FRACTION} subcommand specifies how proportional ranks are to be
1538 calculated. This only has any effect if @subcmd{NORMAL} or @subcmd{PROPORTIONAL} rank
1539 functions are requested.
1541 The @subcmd{PRINT} subcommand may be used to specify that a summary of the rank
1542 variables created should appear in the output.
1544 The function subcommands are @subcmd{RANK}, @subcmd{NTILES}, @subcmd{NORMAL}, @subcmd{PERCENT}, @subcmd{RFRACTION},
1545 @subcmd{PROPORTION} and @subcmd{SAVAGE}. Any number of function subcommands may appear.
1546 If none are given, then the default is RANK.
1547 The @subcmd{NTILES} subcommand must take an integer specifying the number of
1548 partitions into which values should be ranked.
1549 Each subcommand may be followed by the @subcmd{INTO} keyword and a list of
1550 variables which are the variables to be created and receive the rank
1551 scores. There may be as many variables specified as there are
1552 variables named on the @subcmd{VARIABLES} subcommand. If fewer are specified,
1553 then the variable names are automatically created.
1555 The @subcmd{MISSING} subcommand determines how user missing values are to be
1556 treated. A setting of @subcmd{EXCLUDE} means that variables whose values are
1557 user-missing are to be excluded from the rank scores. A setting of
1558 @subcmd{INCLUDE} means they are to be included. The default is @subcmd{EXCLUDE}.
1560 @include regression.texi
1564 @section RELIABILITY
1569 /VARIABLES=@var{var_list}
1570 /SCALE (@var{name}) = @{@var{var_list}, ALL@}
1571 /MODEL=@{ALPHA, SPLIT[(@var{n})]@}
1572 /SUMMARY=@{TOTAL,ALL@}
1573 /MISSING=@{EXCLUDE,INCLUDE@}
1576 @cindex Cronbach's Alpha
1577 The @cmd{RELIABILTY} command performs reliability analysis on the data.
1579 The @subcmd{VARIABLES} subcommand is required. It determines the set of variables
1580 upon which analysis is to be performed.
1582 The @subcmd{SCALE} subcommand determines which variables reliability is to be
1583 calculated for. If it is omitted, then analysis for all variables named
1584 in the @subcmd{VARIABLES} subcommand will be used.
1585 Optionally, the @var{name} parameter may be specified to set a string name
1588 The @subcmd{MODEL} subcommand determines the type of analysis. If @subcmd{ALPHA} is specified,
1589 then Cronbach's Alpha is calculated for the scale. If the model is @subcmd{SPLIT},
1590 then the variables are divided into 2 subsets. An optional parameter
1591 @var{n} may be given, to specify how many variables to be in the first subset.
1592 If @var{n} is omitted, then it defaults to one half of the variables in the
1593 scale, or one half minus one if there are an odd number of variables.
1594 The default model is @subcmd{ALPHA}.
1596 By default, any cases with user missing, or system missing values for
1598 in the @subcmd{VARIABLES} subcommand will be omitted from analysis.
1599 The @subcmd{MISSING} subcommand determines whether user missing values are to
1600 be included or excluded in the analysis.
1602 The @subcmd{SUMMARY} subcommand determines the type of summary analysis to be performed.
1603 Currently there is only one type: @subcmd{SUMMARY=TOTAL}, which displays per-item
1604 analysis tested against the totals.
1612 @cindex Receiver Operating Characteristic
1613 @cindex Area under curve
1616 ROC @var{var_list} BY @var{state_var} (@var{state_value})
1617 /PLOT = @{ CURVE [(REFERENCE)], NONE @}
1618 /PRINT = [ SE ] [ COORDINATES ]
1619 /CRITERIA = [ CUTOFF(@{INCLUDE,EXCLUDE@}) ]
1620 [ TESTPOS (@{LARGE,SMALL@}) ]
1621 [ CI (@var{confidence}) ]
1622 [ DISTRIBUTION (@{FREE, NEGEXPO @}) ]
1623 /MISSING=@{EXCLUDE,INCLUDE@}
1627 The @cmd{ROC} command is used to plot the receiver operating characteristic curve
1628 of a dataset, and to estimate the area under the curve.
1629 This is useful for analysing the efficacy of a variable as a predictor of a state of nature.
1631 The mandatory @var{var_list} is the list of predictor variables.
1632 The variable @var{state_var} is the variable whose values represent the actual states,
1633 and @var{state_value} is the value of this variable which represents the positive state.
1635 The optional subcommand @subcmd{PLOT} is used to determine if and how the @subcmd{ROC} curve is drawn.
1636 The keyword @subcmd{CURVE} means that the @subcmd{ROC} curve should be drawn, and the optional keyword @subcmd{REFERENCE},
1637 which should be enclosed in parentheses, says that the diagonal reference line should be drawn.
1638 If the keyword @subcmd{NONE} is given, then no @subcmd{ROC} curve is drawn.
1639 By default, the curve is drawn with no reference line.
1641 The optional subcommand @subcmd{PRINT} determines which additional tables should be printed.
1642 Two additional tables are available.
1643 The @subcmd{SE} keyword says that standard error of the area under the curve should be printed as well as
1645 In addition, a p-value under the null hypothesis that the area under the curve equals 0.5 will be
1647 The @subcmd{COORDINATES} keyword says that a table of coordinates of the @subcmd{ROC} curve should be printed.
1649 The @subcmd{CRITERIA} subcommand has four optional parameters:
1651 @item The @subcmd{TESTPOS} parameter may be @subcmd{LARGE} or @subcmd{SMALL}.
1652 @subcmd{LARGE} is the default, and says that larger values in the predictor variables are to be
1653 considered positive. @subcmd{SMALL} indicates that smaller values should be considered positive.
1655 @item The @subcmd{CI} parameter specifies the confidence interval that should be printed.
1656 It has no effect if the @subcmd{SE} keyword in the @subcmd{PRINT} subcommand has not been given.
1658 @item The @subcmd{DISTRIBUTION} parameter determines the method to be used when estimating the area
1660 There are two possibilities, @i{viz}: @subcmd{FREE} and @subcmd{NEGEXPO}.
1661 The @subcmd{FREE} method uses a non-parametric estimate, and the @subcmd{NEGEXPO} method a bi-negative
1662 exponential distribution estimate.
1663 The @subcmd{NEGEXPO} method should only be used when the number of positive actual states is
1664 equal to the number of negative actual states.
1665 The default is @subcmd{FREE}.
1667 @item The @subcmd{CUTOFF} parameter is for compatibility and is ignored.
1670 The @subcmd{MISSING} subcommand determines whether user missing values are to
1671 be included or excluded in the analysis. The default behaviour is to
1673 Cases are excluded on a listwise basis; if any of the variables in @var{var_list}
1674 or if the variable @var{state_var} is missing, then the entire case will be